Math 715 - Analysis II - Spring 2005

Meeting Place: HA, Room 261

Meeting Time: T H 11:20-12:35


Instructor: Dr. Demetrio Labate

Office: HA, Room 332

Office Hours: Tue 1:00-2:00 pm, and Thu 10:00-11:00 am. Also by appointment (contact me by e-mail at: dlabate@ncsu.edu or talk to me in class to find a convenient meeting time)



TEXTBOOK: The lectures will mostly follow Real Analysis. Modern techniques and their applications, 2nd Edition, by Gerald B. Folland, Wiley, 1999.

COURSE PURPOSE: This course is an introduction to real analysis and introduces some of the major mathematical tools that are used in applied mathematics, physics, and engineering. For example: the theory of Lebesgue integration is the `right' integration theory in most application from mathematics and physics; functions of bounded variations are widely used in PDE; the theory of Lp spaces spaces is used in PDE and control theory; Fourier analysis is a basic tool in ODE, PDE and engineering. The main topics covered in this course are:

  • Measures.
  • Lebesgue theory of integration, including monotone and dominated convergence theorems.
  • n-dimensional Lebesgue theory of integration, including Fubini's theorem.
  • Differentiation and functions of bounded variations.
  • Theory of Lp spaces.
  • Compact linear operators on normed spaces and spectral theorem.
  • Elements of Fourier analysis.

    HOMEWORK: Homework problems will be assigned every one or two weeks, but will not be collected. Remember: It is strongly encouraged to do the homework problems, since your homework is the most important part of your learning process. Suggested problems:

    Suggested homework problems

    EXAMINATIONS: There will be four take-home tests during the semester and a take-home final exam. It is very important that your work is written in a concise and rigorous manner, as well as in a perfectly readable handwriting (or typed). Tests:

    Test #1 (Due Feb 9)

    Test #2 (Due March 3 (11:25am))

    Test #3 (Due April 5 (11:25am))

    Test #4 (Due April 21 (11:25am))

    Final Exam (Due May 3 (11:25am - Mailbox))

    MAKE-UP EXAMS: There will be NO make-up exams. The attendance policy is consistent with the Academic Regulations which can be found at: http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_regulations/attend/reg.htm (link)

    GRADING: Your overall score will then be determined using the following weights:
    Tests:              80 %
    Final Exam:     20 %

    From the overall score, the final grade will be assigned according to the following set point scale

    A: 88-100, B: 75-87, C: 62-74, D: 49-61, F: 0-48.

    An overall score of 97 or above is guaranteed a grade of A+. There will be a gray area of a few points points below the specified numerical cutoff grades (except 97), within which a +/- system grade will be used. I will also take into account whether your test performance has been improving or declining and your participation to decide whether you get the lower or higher grade.

    ACADEMIC INTEGRITY: Students are expected to follow the University guidelines on academic integrity found in the Code of Student Conduct (link).

    STUDENTS WITH DISABILITIES: Reasonable accomodations will be made for students with verifiable disabilities. In order to take advantage of available accomodations, students must register with the Disability Services at 1900 Student Health Center, campus Box 7509, tel. 515-7653. The NC State policy on working with students with disabilities can be found here.

    LINKS:
    Back to Demetrio Labate Homepage

    Last modified December 16, 2004